EP0986026A1 - Fractal coding of data in the DCT domain - Google Patents
Fractal coding of data in the DCT domain Download PDFInfo
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- EP0986026A1 EP0986026A1 EP98830522A EP98830522A EP0986026A1 EP 0986026 A1 EP0986026 A1 EP 0986026A1 EP 98830522 A EP98830522 A EP 98830522A EP 98830522 A EP98830522 A EP 98830522A EP 0986026 A1 EP0986026 A1 EP 0986026A1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/147—Discrete orthonormal transforms, e.g. discrete cosine transform, discrete sine transform, and variations therefrom, e.g. modified discrete cosine transform, integer transforms approximating the discrete cosine transform
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
- H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
- H04N19/119—Adaptive subdivision aspects, e.g. subdivision of a picture into rectangular or non-rectangular coding blocks
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
- H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
- H04N19/12—Selection from among a plurality of transforms or standards, e.g. selection between discrete cosine transform [DCT] and sub-band transform or selection between H.263 and H.264
- H04N19/122—Selection of transform size, e.g. 8x8 or 2x4x8 DCT; Selection of sub-band transforms of varying structure or type
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
- H04N19/134—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or criterion affecting or controlling the adaptive coding
- H04N19/136—Incoming video signal characteristics or properties
- H04N19/14—Coding unit complexity, e.g. amount of activity or edge presence estimation
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
- H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
- H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
- H04N19/176—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a block, e.g. a macroblock
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/42—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals characterised by implementation details or hardware specially adapted for video compression or decompression, e.g. dedicated software implementation
- H04N19/436—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals characterised by implementation details or hardware specially adapted for video compression or decompression, e.g. dedicated software implementation using parallelised computational arrangements
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/90—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using coding techniques not provided for in groups H04N19/10-H04N19/85, e.g. fractals
- H04N19/99—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using coding techniques not provided for in groups H04N19/10-H04N19/85, e.g. fractals involving fractal coding
Definitions
- This invention relates in general to digital processing systems for recording and/or transmitting pictures, and more in particular to systems for compressing and coding pictures by calculating the discrete cosine transform (DCT) of blocks of pixels of a picture.
- DCT discrete cosine transform
- the invention is particularly useful in video coders according to the MPEG2 standard though it is applicable also to other systems.
- the calculation of the discrete cosine transform (DCT) of a pixel matrix of a picture is a fundamental step in processing picture data.
- a division by a quantization matrix is performed on the results of the discrete cosine transform for reducing more or less drastically the amplitude of the DCT coefficients, as a precondition to data compression which occurs during a coding phase, according to a certain transfer protocol of video data to be transmitted or stored.
- the calculation of the discrete cosine transform is carried out on blocks or matrices of pixels, in which a whole picture is subdivided for processing purposes.
- Such a pre-definition may represent be a heavy constraint that limits the possibility of optimizing the processing system, for example a MPEG2 coder, or its adaptability to different conditions of use in terms of different performance requisites.
- Another important aspect of the invention is a new picture data compressing and coding method that practically is made possible by a hardware structure calculating the DCT on blocks of scaleable size and which essentially consists in
- the AC coefficients are used to decide to which a certain range block belongs: if the sum of their absolute values is less that a determined threshold T , the block range in question is classified as a "low activity” block, on the contrary, if the sum is equal or greater than T , the range block is classified as a "high activity” block.
- the AC coefficients are small and therefore they may be omitted without significantly affecting fidelity: in this case the block may be approximated by storing only its DC coefficient.
- the progression of fractal coding of the invention consists of searching two appropriate linear transform, for example, rotations, ⁇ , overturns, ⁇ or the like and a domain block DCT, of which being defined by F D (u,v) , which at least approximately satisfy the following equation:
- the DCT operation may be defined as follows.
- This figure highlights the transformations performed on the 2x2 block constituted by the pixels (0,6),(0,7),(1,6),(1,7).
- the pixel that constitute the input block are ordered in th e INPUT phase and are processed in the PROCESS phase to obtain the coefficients of the sixteen bidimensional DCT s , or briefly 2-D DCT s , on four samples, for example, the 2-D DCT of the block (0,1) constituted by:
- the coefficients of the 2-D DCT are re-arranged in th e ORDER phase into eight vectors of eight components. For example the coefficients ⁇ a[0],b[0],c[0],d[0] ⁇ constitute the vector l ' .
- the vectors thus obtained proceed to the OUTPUT phase to give the coefficients of the 2x2 DCT, constituting the output block .
- each block ( i,j ) with 0 ⁇ i ⁇ 1 and 0 ⁇ j ⁇ 3 , are ordered to the eight-component vector s l, m, n, o in the following manner:
- each block ( i,j ), with 2 ⁇ i ⁇ 3 and 0 ⁇ i ⁇ 3 , are ordered to constitute the eight-component vector s p, q, r, s in the following manner:
- the pixels of the block ( 0,3 ) will constitute the third component of the l, m, n, o vectors.
- the PROCESS phase consists in calculating in parallel the sixteen 2-D DCT s by processing the eight-component vectors l, m, ..., s as shown in Fig. 5. It should be noticed, for example, that the coefficients of the 2-D DCT of the block ( 0,3 ) will constitute the third component of the vectors a, b, c, d of Fig. 3.
- the ORDER phase consist in arranging the output sequences of the eight 2-D DCT s in eight vectors l', m', ..., s' thus defined:
- the coefficients of the 2-D DCT of the block ( 0,3 ) will constitute the components 4, 5, 6, 7 of the vector m ' .
- This phase consists in rearranging the output data: starting from the eight-component vectors a, b, ..., h , a 64 component vector defined as follows, is constructed:
- the monodimensional DCT or briefly the 1-D DCT, is expressed by the matrix (1-D DCT) 4 given by:
- each quadrant ( i,j ), 0 ⁇ i,j ⁇ 1 are ordered to constitute the vectors:
- the computation of a 4x4 DCT may be subdivided in two stages: consequently, the PROCESS phase that is the only phase in which arithmetical operations are performed, is done twice:
- the variable stage indicates whether the first or second calculation stage is being performed.
- variable stage is updated to the value 0.
- Each MUX receives two inputs:
- This phase consists in processing the l, m, ..., s vectors as shown in Fig. 8.
- the following symbols are used:
- the DEMUX address the data according to two conditions:
- the ORDER phase consists in ranging the output sequence of the eight 1-D DCT s in eight l', m', ...,s' vectors, thus defined:
- variable stage is updated to the value 1.
- the output data from the ORDER phase are sent to the PROCESS phase.
- the processing is subdivided in different steps, to each of which corresponds an architectural block.
- a whole view of the hardware is shown in Fig. 9.
- the pixels of the 8x8 input block are ordered to constitute the eight-component vectors l, m, n, o, p, q, r, s:
- the PROCESS step which is the only phase in which mathematical operations are performed, is performed twice:
- variable stage indicates whether the first or second calculation step is being performed.
- variable stage is updated to the value 0.
- Each MUX receives two inputs:
- This phase consists in processing the l, m, ..., s vectors as shown in Fig. 11.
- the following symbols are used:
- the DEMUX es address the data according to two possibilities:
- This phase consists in arranging the output sequence of the eight 1-D DCT s in eight l', m',...,s' vectors, thus defined:
- variable stage is updated to the value 1.
- the output data from the ORDER phase are sent to the PROCES S phase.
- an algorithm for calculating at choice one 8x8 DCT or four 4x4 DCT s (in parallel) or sixteen 2x2 DCT s (in parallel) may be derived.
- the selection is made by the user by assigning a certain value to the global variable size :
- the object of this phase is to arrange the data to allow the computation starting from the arranged data of the 1-D DCTs. This is done by inputting the luminance values of the pixels (8x8 matrix) and arranging them in eight-component vectors l, m, ..., s.
- PROCESS phase with stage 0
- This phase consists in calculating in parallel the eight 1-D DCT s by processing the vectors l, m, ..., s as shown in Fig. 14.
- the eight MUX es on the right serve to output only the result that corresponds to the pre-selected value of size .
- Fig. 14 may be subdivided into the architectural blocks shown in Fig. 15.
- two vectors each of eight components are input to the QA block, which outputs two vectors of eight components: the first vector is the sum of the two input vectors while the second vector is the difference between the two input vectors that is successively processed with the linear operator A.
- the QA, QB, QC blocks are shown in detail in Figures 16, 17 and 18, respectively.
- the MUX es are controlled by three bits, which correspond to the variable stage (which may take the value 0 or 1, and thus is represented by a bit) and the variable size (which may take the value 0, 1 or 2, and thus is represented by two bits).
- the blocks QD, QE, QF, QG are shown in detail in Figures 19, 20, 21 and 22, respectively.
- the MUX es are controlled by a bit that corresponds to the variable stage .
- the ORDER phase depicted in Fig. 23, consists in arranging the output sequences of the eight 1-D DCT s in eight vectors l', m', ..., s' .
- l', m', ..., s' For example:
- a functional block diagram of a picture compressor-coder according to the present invention may be represented as shown in Figure 1 .
- the compressor-coder performs a hybrid compression based on a fractal coding in the DCT domain. This is made possible by the peculiar architecture of parallel calculation of the DCT on blocks of scaleable size of pixels, as described above.
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Abstract
Description
- subdividing a picture by defining two distinct types of subdivision blocks: a first type, of N/i*N/i dimension called range blocks that essentially are not overimposable one on another, and a second type, of N*N dimension, called domain blocks, that are transferable by intervals of N/i pixels and overimposable one on another (by transferring on the original picture a window that identifies a domain block by an interval equivalent to the horizontal and/or vertical dimension of a range block);
- calculating the discrete cosine transform (DCT) of the 2i range blocks and of a relative domain block in parallel;
- classifying the transform range blocks according to their relative complexity
calculated by summing the three AC coefficients;
applying the fractal transform in the DCT domain to the data of range blocks whose complexity exceeds a pre-defined threshold and storing only the DC coefficient of the range blocks with a complexity lower than said threshold, identifying a relative domain block belonging to the range block being transformed that produces the best fractal approximation of the same range block and calculating its discrete cosine transform; - calculating a difference picture between each range block and its fractal approximation;
- quantizing said difference picture in the DCT domain by using a quantization table predisposed in function of human sight characteristics;
- coding said quantized difference picture by a method based on the probability of the quantization coefficients;
- storing or transmitting the coding code for each range block compressed in the DCT domain and the DC coefficient of each uncompressed range block.
- the DC coefficient that occupies the position 00;
- the three AC coefficients that occupy the positions: 01, 10 and 11, respectively.
- DQ(u,v) is the quantized difference picture in the domain of DCT;
- Q(u,v) is a quantization table designed by considering human sight characteristics;
- INTEG is a function that approximates its argument to the nearest integer;
- INPUT phase
- PROCESS phase
- ORDER phase
- OUTPUT phase.
- the pixels that occupy the position (0,0) in the block constitute the vector l ;
- the pixels that occupy the position (0,1) in the block constitute the vector m ;
- the pixels that occupy the position (1,0) in the block constitute the vector n ;
- the pixels that occupy the position (1,1) in the block constitute the vector o .
- the pixels that occupy the position (0,0) in the block constitute the vector p ;
- the pixels that occupy the position (0,1) in the block constitute the vector q ;
- the pixels that occupy the position (1,0) in the block constitute the vector r ;
- the pixels that occupy the position (1,0) in the block constitute the vector s .
- computation of four 1-D DCT, each performed on an appropriate sequence of four pixels.
- computation of the 2-D DCT starting from said four 1-D DCT.
- a first time, to compute in parallel the sixteen 1-D DCT s ;
- a second time, to compute in parallel four 4x4 DCT starting from the coefficients of the 1-D DCT s .
- a pixel of the original picture, coming from the INPUT phase (this input is selected when stage = 0);
- a coefficient of a 1-D DCT, coming from the ORDER phase (this input is selected when stage = 1).
- if stage = 0, the input datum to each DEMUX is a coefficient of a 1-D DCT; therefore the datum must be further processed and, for this purpose, is conveyed to the ORDER phase;
- if stage = 1, the input datum to each DEMUX is a coefficient of a 2-D DCT; therefore the datum must not be processed farther and therefore is conveyed to the OUTPUT phase.
- the ordering sequences of the pixels of the block of the original picture depend on the chosen DCT size;
- to execute the sixteen 2x2 DCT s the PROCESS step must be carried out only once; instead, to execute the four 4x4 DCT s the PROCESS step must be repeated two times;
- the operations executed during the PROCESS phase are not always the same for the two cases.
- calculating eight 1-D DCTs, each for a certain sequence of eight pixels;
- calculating the 2-D DCT, starting from the eight 1-D DCT s .
- the first time, to compute in parallel sixteen 1-D DCT s ;
- the second time, to compute the 8x8 DCT starting from the coefficients of the sixteen 1-D DCT s .
- a pixel of the original picture, originating from the INPUT phase (this input is selected when stage = 0);
- a coefficient of a 1-D DCT, originating from the ORDER phase (this input is selected when stage = 1).
- if stage = 0, the input datum to each DEMUX is a coefficient of a 1-D DCT; therefore, the datum must be further processed and, for this purpose, is sent to the ORDER phase;
- if stage = 1, the input datum to each DEMUX is a coefficient of a 2-D DCT; therefore, the datum does not need any further processing and therefore is sent to the OUTPUT phase.
- the sequences into which must be arranged the pixels of a block of the original picture depend on the chosen size of the DCT;
- the operations executed during the PROCESS step are not always the same for the two cases.
Claims (4)
- A method of calculating the discrete cosine transform (DCT) of blocks of pixels of a picture, characterized in that it comprises the steps of defining first subdivision blocks called range blocks, having a fractional and scaleable size N/2 i*N/2 i , where i is an integer number, in respect to a maximum pre-defined size of N*N pixels of blocks of division of said picture, referred to as domain blocks, shiftable by intervals of N/2 i pixels, and of calculating the DCT on 2 i range blocks of subdivision of a domain block of N*N pixels of said picture, in parallel.
- The method according to claim 1, characterized in that the calculation of the DCT in parallel on all range blocks of subdivision of a certain domain block is carried out in a hardware structure and comprises the steps of:a) ordering the pixels in function of a subdivision in range blocks of a certain dimension by rearranging the input pixels in a number 2 i of sequences or vectors of 2 i components;b) calculating in parallel 2 i monodimensional DCT s by processing said vectors defined in the preceding step a);c) arranging the output sequences of the monodimensional DCT s relative to said 2 i vectors;d) completing the calculation in parallel of 2 i bidimensional DCT s by processing said output sequences of monodimensional DCT s produced in step c);e) arranging the output sequences of bidimensional DCT s generated in step d) in a number 2 i of vectors of bidimensional DCT coefficients.
- The method according to claim 2, characterized in that the calculation in parallel of said 2 i monodimensional DCT s in step b) and the completion of the parallel calculation of 2 i bidimensional DCT s of step d) are performed by subdividing the sequences resulting from step a) and from step c), respectively, in groups of scalar elements, calculating the sums and differences thereof by way of adders and subtractors and by reiterately multiplying the sum and difference results by respective coefficients until completing the calculation of the relative DCT coefficients, respectively monodimensional and bidimensional.
- A method of compressing data of a picture to be stored or transmitted through a fractal coding, characterized in that the fractal transform is carried out in the domain of the discrete cosine transform (DCT) through the following steps:subdividing a picture in blocks of pixels of said two distinct type of blocks as defined in claim 1;parallely calculating the discrete cosine transform (DCT) of all the 2 i range blocks and of a relative domain block;classifying the transformed range blocks according to their relative complexity represented by the sum of the values of the three AC coefficients;applying the fractal transform in the DCT domain to the data of the range blocks whose complexity classification exceeds a pre-defined threshold and storing only the DC coefficient of the range blocks with a complexity lower than said threshold, identifying a relative domain block to which the range block in a transformation belongs that produces the beset fractal approximation of the range block;calculating a difference picture between each range block and its fractal approximation;quantizing said difference picture in the DCT domain by using a quantization table preestablished in function of the characteristics of human sight;coding said difference picture quantized by a process based on the probabilities of the quantization coefficients;storing or transmitting the coding code of each range block compressed in the DCT domain and the DC coefficient of each uncompressed range block.
Priority Applications (2)
Application Number | Priority Date | Filing Date | Title |
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EP98830522A EP0986026A1 (en) | 1998-09-07 | 1998-09-07 | Fractal coding of data in the DCT domain |
US09/390,554 US7233623B1 (en) | 1998-09-07 | 1999-09-03 | Method and scalable architecture for parallel calculation of the DCT of blocks of pixels of different sizes and compression through fractal coding |
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EP98830522A EP0986026A1 (en) | 1998-09-07 | 1998-09-07 | Fractal coding of data in the DCT domain |
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Cited By (3)
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SG157954A1 (en) * | 2001-06-29 | 2010-01-29 | Qualcomm Inc | Dct compression using golomb-rice coding |
CN117241042A (en) * | 2023-08-31 | 2023-12-15 | 湖南大学 | Fractal image compression method and system for classifying image blocks by DCT |
CN117241042B (en) * | 2023-08-31 | 2024-05-14 | 湖南大学 | Fractal image compression method and system for classifying image blocks by DCT |
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US7574055B2 (en) * | 2004-09-07 | 2009-08-11 | Lexmark International, Inc. | Encoding documents using pixel classification-based preprocessing and JPEG encoding |
WO2010134079A1 (en) * | 2009-05-20 | 2010-11-25 | Nissimyan, Nissim | Video encoding |
US9215470B2 (en) | 2010-07-09 | 2015-12-15 | Qualcomm Incorporated | Signaling selected directional transform for video coding |
US10992958B2 (en) | 2010-12-29 | 2021-04-27 | Qualcomm Incorporated | Video coding using mapped transforms and scanning modes |
RU2541203C2 (en) * | 2013-06-25 | 2015-02-10 | Государственное казенное образовательное учреждение высшего профессионального образования Академия Федеральной службы охраны Российской Федерации (Академия ФСО России) | Method of compression of graphic file by fractal method using ring classification of segments |
US10306229B2 (en) | 2015-01-26 | 2019-05-28 | Qualcomm Incorporated | Enhanced multiple transforms for prediction residual |
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US11323748B2 (en) | 2018-12-19 | 2022-05-03 | Qualcomm Incorporated | Tree-based transform unit (TU) partition for video coding |
CN114022580B (en) * | 2022-01-06 | 2022-04-19 | 苏州浪潮智能科技有限公司 | Data processing method, device, equipment and storage medium for image compression |
CN115348453B (en) * | 2022-10-14 | 2023-01-24 | 广州市绯影信息科技有限公司 | Full-parallel fractal coding method and system for aerial images |
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Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
SG157954A1 (en) * | 2001-06-29 | 2010-01-29 | Qualcomm Inc | Dct compression using golomb-rice coding |
CN117241042A (en) * | 2023-08-31 | 2023-12-15 | 湖南大学 | Fractal image compression method and system for classifying image blocks by DCT |
CN117241042B (en) * | 2023-08-31 | 2024-05-14 | 湖南大学 | Fractal image compression method and system for classifying image blocks by DCT |
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